In our first project, we analyzed daily weather patterns from data collected at a weather station in Central Park, New York City made available online by the National Oceanic and Atmospheric Administration. Through our analysis, we confirmed that there was a statistically significant rise in daily maximum temperatures in Central Park over the last 122 years.
We performed an ANOVA test on daily maximum temperature values over different periods of time and found statistically significant results regarding variance in-between our samples. This led us to create linear models for the change in daily maximum temperature over time, revealing statistically significant warming at an average rate of about 0.025 degrees Fahrenheit per year from 1900-2022. This is in fact a larger increase in temperature than the average global warming trend reported by [INSERT ORGANISATION NAME HERE!] (an average of 0.014 degrees Fahrenheit per year). However, since 1982, average temperatures in Central Park have increased significantly less than average global warming, perhaps because much of the development in New York City took place during the first half of the century.
We had more questions about relationships between weather and human activity, which are explored here in our Final Project.
For this project, we looked more directly at correlations between human activity and weather by incorporating new datasets related to population, air quality, crime (shootings and arrests), the stock market, and COVID-19.
We developed several linear models of Central Park warming over time in Project 1 using all daily TMAX observations between 1900 and 2022. We observed statistically significant correlations between month (as a categorial variable), reflecting seasonal temperature variations, and year (as a numeric variable), reflecting a longer-term warming trend.
The resulting fit (using all daily data) has an \(R^2\) value of 0.775 and a slope of 0.025 degrees Fahrenheit per year, with all fit parameters’ p-values well below 0.05. The different intercepts for the each level of the categorical variable (the twelve months of the year) indicated that January is the coldest and July the hottest month in Central Park, with an average difference in maximum daily temperature of approximately 46 degrees Fahrenheit in any given year over this window.
The two extremes and their linear models are plotted again here to illustrate the quality of fit.
However, we expect that time is just a proxy for the cause: human activity– namely, construction in the local environment using materials that hold more heat than the natural environment (EPAb 2022), and increased consumption of energy and materials that release greenhouse gases over the course of their life cycle. We wanted to explore correlations with other, more direct proxies for human activity.
We sought other data sources related to these trends, for example local economic data (New York GDP), construction (sector revenue or number of new sites), New York City population, and local GHG emissions. While we found some sources for most of these, unfortunately none extended more than 50 years into the past with daily or annual observations except one: annual New York State population data (obtained from Macrotrends.com). Because this source was unknown, we validated the reported value for each decade against the corresponding data from the U.S. Census (it appears that values for intervening years were interpolated somehow).
We then recreated a new linear model for TMAX (for 1900-2021 due to
range of population data), attempting to use New York State
population instead of year: ‘TMAX ~ population +
month’.
While we do observe a significant correlation – the p-value of the
model’s population coefficient is well below the cutoff of
alpha = 0.05) – the fit appears not to be any better than the regression
against year. This caused us to wonder if a fit using month alone would
be better than a fit using month or year, or
population or year.
The \(R^2\) value is a bit lower
(though not much: 0.771 v. 0.773). To assess whether the model is
distinct from those also including population or
year, we ran ANOVA tests on each pair of nested models.
According to the tests, the models are in fact significantly different
(p-values of the chi-squared fits were well below an alpha of 0.05).
Nonetheless, given that the data are partially interpolated values and that we are looking at subtle, long-term trends over only 122 years at a single location– and that climate change is a complicated, average, and distributed phenomenon– we have probably exhausted our ability to build climate change models based solely on Central Park data.
For fun, we looked for correlations between temperature and other weather variables between 1900 and 2022.
We do see some correlation between TMAX and
SNOW, and so add this into the model
(TMAX ~ year + month + SNOW). This is slightly improved
(with all coefficients’ p-values well below 0.05): year, month, and
whether it is snowing appear to account for 77.6% ($R^2 = 0.776) of the
variability of in daily maximum temperature in Central Park. (However,
we note that 96 NAs for SNOW had to be removed to develop
the model, so this result is likely not directly comparable to the other
models). We also considered additional local environmental correlations,
described in the next section.
The Air Quality Index (AQI) is used for daily reporting of local air quality. It tells us how clean or polluted the air is, and what associated health effects might be a concern for the public. The higher the AQI value, the the greater the level of air pollution and greater the health concern. Outdoor concentrations of pollutants such as ozone, carbon monoxide, nitrogen dioxide, sulfur dioxide, and PM2.5/PM10 concentrations are measured at stations across New York City and reported to the EPA. The daily AQI is calculated based on these concentration values and stored within the EPA’s Air Quality System database.
Changes in urban life correlate with changes in air quality within that urban area. Sources of emissions such as traffic and burning of fossil fuels for energy generation can cause air quality to deteriorate. Emissions can also contribute to global warming by releasing more greenhouse gasses into the atmosphere, thus increasing average temperatures. As more people migrate to urban areas, we will continue to see a deterioration in air quality unless reducing measures are taken. Our goal for integrating this data is to study the affects of weather patterns on air quality, and to statistically verify changes in air quality over time in New York City.
The dataset contains about 7,000 observations collected from January, 2000 to October, 2022.
We start by looking at the distribution of our variable of interest: AQI.
From the histogram above, we can gauge that the distribution is slightly right-skewed. With the large number of observations in our dataset, we can assume normality for our modeling. The right-skewness is caused by days with unusually high AQI values.
The year-over-year growth rate was also calculated based on yearly average AQI and is depicted in the line plot below.
We can see an alternating patterns of increase and decrease in average AQI between each year from 2000 to 2009. After 2009, the pattern is broken but the variance continues.
In order to evaluate correlation between weather and air quality, we combined our dataset with the NYC weather data based on the date value in each. Dates without a matching air quality measurement are dropped. Subsequent models will be built using this merged dataframe.
The first step to building linear models is assessing correlation between numerical variables in the data. Because the year variable in our dataset begins at 2000, it will unnecessarily scale our coefficients when used in linear modeling. Therefore, we scaled the variable to start at 0 (and continue to 22 to represent 2022).
The correlation is evaluated via a pairs plot, which depicts the correlation coefficient between numerical variables, and includes scatterplots of their relationships. The pairs plot uses the Pearson correlation method.
From the pearson pairsplot above, we can see a moderately high, negative correlation value between year and AQI. This indicates that as the year increases, the AQI is actually dropping resulting in better air quality in the city.
To better observe the effects of year on AQI, we can visualize the yearly average AQI.
The line plot confirms the correlation value we observed in the pairs plot. The average yearly AQI is indeed decreasing as year increases. Next, we build a linear model using year as a regressor to estimate daily AQI.
The results of our linear model reveal a significant value for both the intercept and year coefficient. The coefficient value for the year regressor indicates that for every year increase, the predicted daily AQI decreases by a factor of 1.78. This supports the correlation coefficient we saw earlier between these two variables. The p-value of the F-statistic is also significant, but the \(R^2\) value of the model is a measly 0.28. Based on this model, the year only explains 28% of the variability in daily AQI measurements. This is not a significantly high result. Looking at the scatterplot of the relationship can help explain the weak fit.
As we can see, there is a high degree of noise when observing daily
AQI values at the yearly level. Although the plot displays a slightly
downward trend in daily AQI, but model fit is distorted. This helps
explain the results we received from our linear model.
Can we add more or different predictors to improve the fit? In our first
project, we looked at linear trends of TMAX over time and determined a
slight positive correlation observed over the years 1900-2022. We also
utilized month as a categorical regressor to help explain the variance
in daily maximum temperatures. Based on those results, we concluded that
seasonality trends had a negative impact on model performance. Perhaps
seasonality also also plays a part in daily AQI measurements.
To refresh our memories, we included the monthly average daily maximum temperature. A seasonal trend can be observed as temperatures increase during summer months and decrease during winter months.
Plotting the average AQI by month, we observe seasonal trends. AQI values are generally high during winter and summer months, but realtively low for the the months in between.
Based on this, we modify our last model and attempt to fit
seasonality by adding month as a categorical regressor,
along with our variable-of-interest from the last project -
TMAX.
The regression coefficient for TMAX is significant and
positively correlated, with each degree Fahrenheit increase resulting in
AQI increasing by a factor of 0.68. The regression coefficients for all
month categories are also significant. In fact, every month has a
negative impact on AQI when compared to January. September exhibits the
largest difference, with a predicted AQI almost 44 points lower than
January!
The p-value of the model’s F-statistic is also significant,
concluding a significant relationship between our chosen predictors and
the daily AQI value. However, the \(R^2\) for our model is only
.149, which is weaker than our previous model. This
indicates that only 14.7% of the variation in daily AQI can be explained
by TMAX and month.
The VIF scores for all regressors are in an acceptable range, however the fit is still poor. It seems that due to seasonal nature of our time-series data, we cannot properly model daily AQI using linear regression. Perhaps a classification technique can be utilized to address the seasonal trends. More precisely, we can build a kNN model to classify the month based on daily AQI and maximum temperature values.
We start with plotting the relationship between our chosen predictors and add a layer to discern month within the plot.
We can make out minimal distinction of month from the scatterplot above, but the model will provide a more detailed analysis.
The first step involves scaling and centering our predictor values, as they are recorded in vastly different units of measurement. We also need to split our dataset into training and testing frames. We used a 4:1 split for to satisfy this requirement.
To find the optimal k-value, we evaluated the model over a range of k from 1 to 21. Based on the plot above, it seems 13-nearest neighbors is a decent choice as it provides the greatest improvement in predictive accuracy before the incremental improvement trails off. We can build the kNN model using 13 as the k-value.
The overall accuracy of our model is a relatively weak value of 0.257. This indicates that AQI and TMAX are not good predictors of month.
## Multi-class area under the curve: 0.644
A multi-class ROC evaluation on the test labels yields an AUC value of 0.65, which is higher than expected based on the model’s accuracy value. Still, this is not a significant result based on the AUC threshold of 0.8.
Overall,we have identified statistically significant correlations between weather, air quality, and human activity data from NYC– but none of our models demonstrate high predictive potential.
We were unable to develop a model for Central Park warming on a century scale, due to a lack of quality data over this time frame that accounted for relevant human activities (such as expansion of the built environment, local population or greenhouse gas emissions on a daily basis). This work has given us a new appreciation of just how complicated weather and climate models must be– especially if they are to be used predictively.
In our air quality analysis, our hypothesis that a correlation would exist between daily weather and air quality variables was ultimately proven wrong. We observed trends of declining AQI over time, but the explanation of variance from our model results was not strong enough to deem the model a good fit. Similarly, a linear model predicting AQI based on the categorical month variable, along with TMAX, also resulted in a poor fit.
We determined that the relationship between air quality and global warming is difficult to model using linear techniques due to seasonal trends in the variables. Our attempt to model the effect of these trends using kNN also resulted in a poor-fitted model. Ultimately, a different type of model would be required to address the seasonal component.
Also, changes in climate are slow to take effect. A increase in emissions does not necessarily lead to increases in temperature on the same time scale. All these effects would need to be taken into consideration for an effective analysis.
We did identify correlations between daily weather and local human activity in some areas. Both crime and stock market trade volume had statistically significant correlations to daily weather variables in our linear models. Crime (daily numbers of shootings and arrests) is correlated to both temperature and precipitation while stock market trade volume is related to temperature. However, models based on these correlations are not strong or complete enough to be predictive.
Observed correlations between crime and weather were the strongest we found in this analysis. This represents a valuable area for future study in the context of changing weather patterns that was explored in our early project.
There were notable limitations to the methods in this analysis. One key limitation that affected the analysis of public health was the availability of essential data. The COVID-19 case data was based on dates when positive cases were confirmed, rather than tested. Because test and confirmation dates are not always the same, this limited our ability assess relationships that existed on the day of an individual’s test. Looking for alternative data sources to explore this relationship would be an interesting area for a future project. From our results, we also conclude that linear models might not be optimal for representing data with seasonal trends.
These questions are only some of the important questions that should be asked about the relationship between humans, weather, climate, and the environment. As climate change continues, it will be increasingly important to continue to study its effects on people, from the global scale down to local communities around the world.
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